The need for shorts largely goes away if you make stock buyers hold for at least a year before selling.
Remember, the purpose of the market is as a funding mechanism for companies to pursue growth and innovation, not to allow a bunch of "banksters" to game the system. That means that investment should always be longish-term. So let's make their stupid games not worth playing.
FWIW, If you do allow intra-day trading, applying a random delay of up to, say, four hours would eliminate most of the problems...